Thermodynamics: At a temperature of $15\backslash$deg C there is $3$ bar pressure left in a bicycle wheel. It gets pumped up with a bicycle pump $($Length: $48$ cm$,$ cross$-$section surface: $5$ cm$^2).$ The air is treated as an ideal gas, so pV $=$ nRT can be used.

a$)$ How many particles go through the pump using the pump once at $1$ bar

b$)$ How far do you need to press the pump $($how many of the $48$ cm are needed$)$ to reach $3$ bar pressure within the pump at constant temperature?

c$)$ Calculate the amount of work that is needed to compress the air from the $1$ bar to $3$ bar?

d$)$ In which forms of energy gets the work transformed?

e$)$ Calculate the amount of work that is needed to press the compressed air $(3$ bar$)$ against the $3$ bar within the wheel.

If not everything can be answered, its okay :) Thanks a lot! Pls with a bit explanation :)